Find the value of x

Question

Find the value of x.

Show all calculations and an explanation as to whether or not your answer is reasonable. Leave your answer in simplest radical form. 

Answer 1

Here's the Theorem you need to solve this problem:

When two secants intersect outside a circle, the degree measure of the angle they form is one-half the difference of the degree measure of their intercepted arcs

The degree measure of the angle formed by the secants is 10°. One of the intercepted arcs is 30°. Label the other as y. Using the theorem:

10° = (30°-y)/2

Solving for y, we get, y = 10°. From the diagram, we have 30° + x + 10° = 180°. Solve for x.